3.4 Leg controller organization
3.4.2 Neural Phase Generator (NPG)
First an overview of the NPG structure is given by listing the neurons constituting the NPG and explaining their role. Sensory informations used to regulate the transitions between the modules are then presented. The parameters settings for the NPG are given in Section B.2.2.
3.4.2.1 Neuronal structure
The NPG is the part of the leg controller responsible for the rhythm generation and is made of functional units called “modules”, accounting for the main phases of the locomotion. It is constituted of two modules, the flexor and extensor modules, each
QF
T2F T1F HF
Flexor Module
QE
HE T1E T2E
Extensor Module
NFF PFF IPF
AEP IPE PFE
Leg Loading
PEP
NFE
phase signal to MOSS
phase signal to MOSS
excitatory inhibitory
0 0.2 0.4 0.6 0.8
Extensor Module
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1
0 0.2 0.4 0.6 0.8
Flexor Module
H Q IP
T2 T1
PF NF
Time [s]
Neuronal activity
Figure 3.4: Internal structure of the NPG (up) and activity of its constitutive neurons during one walking cycle (down). The NPG is made of two modules, the flexor and theextensor modules, representing the two phases of the locomotor cycle. Transition of activity (represented by the activity level of H neuron) from module to the other occurs through the successive activation of the transition neuronsT1 andT2, this later finally activating theH neuron of the next module. This process is under the control of sensory feedback, through excitatory and inhibitory influences mediated by the sensory neurons P F and N F. The corresponding neuronal activities during locomotion are
represented (the locomotion speed is around 0.6 m/s).
of them accounting for the corresponding phase observed in animal locomotion (as ex-plained in Section 2.2.1). The activity of the NPG characterizes the current phase of the locomotion of the leg. As represented in Figure 3.4, each module of the NPG is composed of seven neurons (all of them are interneurons, except P F and N F that are sensory neurons, see Appendix B.1 for details):
H neuron is the neuron representative for the activity of the module. It has excitatory connections with itself (self-excitation), as well as with theQandT1 neurons. On the other hand, it inhibits theIP neuron.
Q neuron ensures that only one module is active at the time by inhibiting theH and T neurons of the other modules.
T neurons are responsible for the transition to the next module. Two transition neu-rons are implemented5: a slow T1 neuron which receives excitatory inputs from both theH neuron and the sensory feedback pathways (through the P F neuron) and a fast T2 neuron, which is under inhibitory sensory influence (through the N F neuron). T1 excitesT2 neuron which then promotes transition by exciting the H neuron of the next module, while reducing its inhibition by inhibiting the Q neuron of its own module. T2 also inhibits the H neuron of its own module, in order to reduce the simultaneous activation of the twoH neurons (hence reducing the simultaneous activation of the synergies at the MOSS level). This structure allows to set the time constantτ ofT1in order to achieve long duration of module activity without slowing down the transition when inhibitory sensory input acting on T2 disappears.
IP neuron is the complementary neuron ofH: it is active when the module is inactive.
This neuron has inhibitory connections to the interneurons in the MOSS and its output is used to select the synergies that can be active during the phase of the locomotion represented by the module to which theIP neuron belongs. Accord-ingly, theIP neuron of the flexor phase inhibits the liftoff and the swing synergies, while the one of the extensor phase inhibits the touchdown and the stance syn-ergies. When H becomes active, it inhibits IP, hence it activates the previously inhibited synergies. TheIP neuron additionally plays a gating role of the sensory feedback that promote the transition by inhibiting theP F neuron. IP receives a constant excitatory input from a tonic neuron not represented on the figure.
P F and N F neurons are sensory neurons that relay the sensory signals to the tran-sition neuronsT1 andT2. P F is used for the sensory feedback which promotes the transition andN F for the sensory feedback which prevents it.
5In the NPG model of Wadden and Ekeberg (1998)(62), there was only oneT neuron per module, receiving only excitatory sensory inputs.
Activity of these neurons for both modules during one locomotor cycle is represented on Figure 3.4. Alternative activation of H, Q and IP can be observed, as well as the activation of T1 andT2 induced by the sensory feedback relayed byP F and N F. Using this NPG structure, the regulation of the transition of activity from one module to another depends on two factors:
• the intrinsic properties of the neurons of the neural pathway involved in the tran-sition (H→ T1 → T2), as well as the synaptic weights of the connections between them;
• the excitatory and inhibitory influences to theT neurons based on sensory feedback and mediated respectively by the neuronsP F and N F
The relative contributions of these two components can be adjusted to get either a more oscillator CPG model (when the first component is predominant) or a more sensor-dependent CPG model (when it is the second one that prevails). To comply with the common principles defined in Chapter 2, the parameters were set in order to get a sensor-dependent CPG. In particular, the synaptic weight of the excitatory connection fromH to T1 is set in order that the excitatory input coming from neuron H is insufficient to induce alone T1 activity. In that case, the NPG does not naturally oscillate and the phase transitions are completely under the control of the sensory information relayed by P F and N F.
3.4.2.2 Sensory information used for the regulation of the phase transitions
The same kinds of sensory information as Ekeberg and Pearson (2005)(17) were used to regulate the transition of activity between the NPG phases.
The transition from the flexor to the extensor phase is triggered when the leg is getting close enough from the desired anterior extreme position (AEP). This is evaluated using the length of the extensor muscle of the most proximal joint of the leg (i.e. AB for the hind legs andLDfor the forelegs). As the muscle length increases,T1F is progressively activated by the input coming from P FF. On the other hand,N FF is active as long as the muscle length is smaller than a certain threshold. When the threshold is reached, inhibition ofT2F disappears and the transition occurs.
On the other hand, the transition from the extensor to the flexor phase is regulated using two conditions based on sensory information:
• the leg must be close enough to the posterior extreme position (PEP). This is evaluated using the length of the flexor muscle of the most proximal joint of the leg (i.e. IP for the hind legs and BC for the forelegs). As the muscle length increases, T1E is progressively activated by the input coming from P FE.
• the leg must be unloaded (Leg Loading). Estimation of the leg loading is given by the muscular force developed by the most distal extensor muscle (i.e. Sol for the hind legs andT for the forelegs). As long as it is over a certain threshold,N FE is activated and the transition is prevented.